OSHA was created by statute and can’t be done away with by a President.
Xiden isn’t doing away with anything.
Despite Xiden’s position to the contrary, they are applying the statute into an area Congress’ did not put into the statute. And even if Congress did put it in the statute, then the question would be whether it is constitutional. If you really want to see what the demonkkkraps think about the issue, if the roles were reversed and Trump were trying to do this ... the demonkkkraps would be against it as unconstitutional. The anti-demonkkkraps** would continue to be against it.
(** - I am moving away from calling people on the political right “conservatives”, because the way things have been run for over 5 decades, and maybe more, I don’t want to conserve any of it.)